Well, what's fun is that (AFAIK) trigonometric functions tend not to be implemented in the newer floating point instructions, such as AVX or SSE.
So while what you say is true about the x87 implementation of those functions, for anything targeting a machine built in the last 20 years it's likely the code will run consistently regardless the architecture (barring architecture floating point bugs, which aren't terribly uncommon in the less significant bits and when overclocking comes into play).
x86 compilers won't use x87 instructions when SSE2 and later are available. x87 is just a really weird and funky instruction set that's best left in the gutter of history.
So while what you say is true about the x87 implementation of those functions, for anything targeting a machine built in the last 20 years it's likely the code will run consistently regardless the architecture (barring architecture floating point bugs, which aren't terribly uncommon in the less significant bits and when overclocking comes into play).
x86 compilers won't use x87 instructions when SSE2 and later are available. x87 is just a really weird and funky instruction set that's best left in the gutter of history.